Bahasa Inggris dalam Pembelajaran Matematika

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KAKTAT PENGAGNTN ATR Puji syukur kami panjatkan ke hadirat Tuhan Yang Maha Esa, karena atas karunia-Nya, bahan ajar ini dapat diselesaikan dengan baik. Bahan ajar ini digunakan pada Diklat Guru Pengembang Matematika SMK Jenjang Dasar Tahun 2009, pola 120 jam yang diselenggarakan oleh PPPPTK Matematika Yogyakarta. Bahan ajar ini diharapkan dapat menjadi salah satu rujukan dalam usaha peningkatan mutu pengelolaan pembelajaran matematika di sekolah serta dapat dipelajari secara mandiri oleh peserta diklat di dalam maupun di luar kegiatan diklat. Diharapkan dengan mempelajari bahan ajar ini, peserta diklat dapat menambah wawasan dan pengetahuan sehingga dapat mengadakan refleksi sejauh mana pemahaman terhadap mata diklat yang sedang/telah diikuti. Kami mengucapkan terima kasih kepada berbagai pihak yang telah berpartisipasi dalam proses penyusunan bahan ajar ini. Kepada para pemerhati dan pelaku pendidikan, kami berharap bahan ajar ini dapat dimanfaatkan dengan baik guna peningkatan mutu pembelajaran matematika di negeri ini. Demi perbaikan bahan ajar ini, kami mengharapkan adanya saran untuk penyempurnaan bahan ajar ini di masa yang akan datang. Saran dapat disampaikan kepada kami di PPPPTK Matematika dengan alamat: Jl. Kaliurang KM. 6, Sambisari, Condongcatur, Depok, Sleman, DIY, Kotak Pos 31 YK-BS Yogyakarta 55281. Telepon (0274) 881717, 885725, Fax. (0274) 885752. email: [email protected] Sleman, 11 Mei 2009 Kepala, Kasman Sulyono NIP. 130352806 Daftar Isi Kata Pengantar ------------------------------------------------------------------------------------ i Daftar Isi ---------------------------------------------------------------------------------------ii Kompetensi/Sub Kompetensi dan Peta Bahan Ajar ------------------------------------- iii Skenario Pembelajaran ------------------------------------------------------------------------- iv Unit 1 Numbers -------------------------------------------------------------------------- 1 Unit 2 2-Dimensional ------------------------------------------------------------------- 5 Unit 3 Reading --------------------------------------------------------------------------13 iiKOMPETENSI Mampu memahami literatur berbahasa Inggris. SUB KOMPETENSI Memiliki kemampuan membaca dan menjelaskan hal-hal yang berkait dengan bilangan dalam bahasa Inggris. Memiliki kemampuan membaca dan menjelaskan hal-hal yang berkait dengan geometri dimensi dua dalam bahasa Inggris. Memiliki kemampuan membaca artikel dalam bahasa Inggris serta dapat menentukan beberapa point penting pada artikel tersebut. PETA BAHAN AJAR Mata diklat untuk jenjang dasar ini membutuhkan pengetahuan prasyarat berupa pengetahuan bahasa Inggris dasar. Pada diklat jenjang dasar ini kepada para peserta hanya diberikan pengetahuan yang berkait dengan bilangan dan istilah pada geometri dimensi dua (geometri datar). Pada diklat tahap lanjut dan menengah, kepada para peserta diharapkan sudah lebih mampu memahami buku maupun literaratur berbahasa Inggris. iiiSKENARIO PEMBELAJARAN Penyampaian Mtr (60’) Pendahuluan (5’) Mempelajari Tujuan Bilangan (Numbers) Ruang Lingkup Geometri Datar (2- Langkah-langkah Dimensional) Penugasan (45’) Membaca artikel dalam Laporan (20’) bahasa Inggris Menemukan tiga point pada Hasil diskusi artikel tersebut Masalah Penutup (5’) Rangkuman Refleksi Tugas ivUnit I Introduction A. Rationale English is very important, not only for students of SMK (Secondary Vocational School); but also for mathematics teacher of secondary vocational school. The reason is, there are a lot of mathematics or mathematics education books, periodicals, jurnals, video cassette recorders, or films, are written ot talked in english such as: o The Art of Algebra by Abrahamson, D; Gray, M.C. (1971). Adelaide: Rigby Limited. o 40 Investigational Work, by Bastow, B.; Hughes, J.; Kissane, B.; & Randall, R.; (1984). Perth: Mawa. o Dictionary of Mathematics by Borowski, E.J.; Borwein, J.M. (1989). London: Collins o 7th International Congress on Mathematical Education (ICME-7). Topic Group 10: Constructivist Interpretations of Teaching and Learning Mathematics. Perth: Curtin University of Technology. o An Introduction to Matrices,Vectors, and Linear Programming (2nd Ed) by Campbell, H.G. (1977). New Jersey: Prentice-Hall, Inc. o Dynamics of Teaching Secondary School Mathematics by Cooney, T.J.; Davis, E.J.; Henderson, K.B. (1975). Boston: Houghton Mifflin Company. o Introduction to Logic by Copi, I.M. (1978). New York: Macmillan. o What is Mathematics by Courant, R.; Courant, H. (1981) Oxford University Press: Oxford. o Mathematical Literacy for Living from OECD-PISA Perspective by De Lange, J. (2005). Paris: OECD-PISA. In addition, some of Secondary Vocational School has been or will be declared to be Schools Based International (Sekolah Berwawasan Internasional = SBI). In those schools, english is used or will be used during the teaching and learning process. In anticipating the situation, mathematics teacher should be provicient in english, written or orally. In other to fulfill the needs, during the inservice training, one of the topic is ‘Bahasa Inggris dalam Pembelajaran Matematika’ or ‘English in Teaching Mathematics.’ This materials will be used during the session. B. Objectives The general aim of the session is to help mathematics teacher to understand english literature especially in mathematics and mathematics education literature. After the session, the participant will be able to: Read and explain the materials concerning numbers. Read and explain the materials concerning 2-Dimensional Geometry Read and explain the articles written in english. C. The Used of Materials The materials are written in such a way that can be learned by participants by themselves. Ideally, the materials can be learned before the session. During the session participants can ask to the tutor (Widyaiswara) about those materials, especially the spoken problems. Unit 2 Numbers A. 17 (seventeen) is an example of a number. It is a whole number or integer. A number consists of one or more digit. 13, 5, and 35 are odd numbers; while 2, 4, and 18 are even numbers. • When we add one quantity to another we use the symbol ‘+’ (plus). The name of this operation is addition. The result of this operation is called the sum. • When we subtract one quantity to another we use the symbol ‘−’ (minus). The name of this operation is subtraction. The result of this operation is called the difference. • When we multiply one quantity to another we use the symbol ‘×’ (multiplied by or times). The result of this operation is called the product. • When we divide one quantity to another we use the symbol ‘:’ (divided by). The name of this operation is division. The result of this operation is called the quotient. • The result of these operation are indicated by the symbol = (equals). Practice 1.A 1. Read out the following a. 6 b. 34 c. 578 d. 9.573 e. 812.934 f. 1.234.567 g. 9 + 7 = 16 h. 78 − 24 = 54 i. 14 × 27 = 378 j. 36 : 9 = 4 2. Fill in the blank spaces in the following sentences by using single words. a. The ---- of three and four is seven. b. The operation which uses the symbol “×” is called ---- . c. Twelve ---- six equals two. d. The result of a subtraction problem is called the ---- . e. An integer is also known as a ---- . f. Any number consists of combination of ---- . g. Seventeen subtracted ---- twenty equals ---- . h. Seven multiplied ---- five equals ---- . i. When we ---- two quantities, for example eight plus twelve, the answer (twenty) is called the ---- . j. The product is the result when one quantity is ---- another 4B. (four fifths or four over five) is an example of a fraction. In this fraction, 4 is the 5164numerator and 5 is the denominator. is an improper fraction. 4 is a mixed 55number. 2To add or to subtract vulgar fraction, we must express them in terms of the lowest 21common denominator. For example (e.g.) in this subtraction − , the lowest common 35denominator is 15. 223To multiply or divide vulgar fraction e.g. 2× 2 ×1 , we must first change the mixed 3548127number to improper fraction ×× and then cancel where it is possible. Then 354multiply the numerators and the denominators and express the result as a mixed number. 1To write a decimal fraction we use a decimal point. For example, if we convert 2 into 42a decimal fraction, the result is 2,25 (two point two five). if we convert into a decimal 3fraction, the result is 0, 6 (nought point six recurring). 17 : 3 = 5, 6 or 5,67 correct to two decimal places, while π is equal to 3,142 correct to four significant figures. Practice 1.B 1. Read out the following 11719a. h. 3+ 2= 5 2410201217b. i. − = 335151111c. j. − = 468242k. 81,355 d. 13l. 3,6 + 7,2 = 10,8 11m. 10 : 6 = 1,6 e. × 53n. 655 : 3 = 218,3 13o. 6,5 × 42,6 = 276,9 f. × p. 781,9 + 63,5 = 845,4 35 72g. ÷ 43 2. Using single words, fill in the blank spaces in the following sentences: a. In the vulgar fraction seven ninths, ---- is the denominator and ---- is the ---- . b. To ---- a vulgar fraction to a decimal fraction, we simply ---- the numerator by the denominator. c. The ---- ---- ---- of two third and a half is six. d. An integer plus a fraction makes a ---- ---- . e. An improper fraction exists when the ---- is greater than the ---- . f. To multiply a decimal fraction by ten, we simply move the ---- ---- one place to the right. g. 57,074 correct to ---- ---- ---- is 57,1. 3h. To add or subtract vulgar fraction, we must ---- them in ---- ---- their lowest common denominator. i. To devide a decimal fraction by ---- we simply move the decimal point one ---- to the ---- . 525j. × becomes if we ---- the two’s. 299 C. If in a given classroom, there are fourteen boys and seven girls, we say that the ratio of girls to boys is 1 : 2 (one to two). When we build a model ship, we make it to scale. For example, if a model is built to scale of 1 : 30 (one to thirty), this mean that 10 centimeters on the model represent 300 centimeters on the ship itself. The scale of a map shows the ratio of the distance on the map to the distance on the area covered by the map. On a map this ratio is called the representatives fraction. 3 : 6 (three to six) and 5 : 10 (five to ten) are two equal ratios, in other words 3,6 and 5,10 are in proportion, in direct proportion, or directly proportional. If it takes 5 men one hour to do a job, and 10 men half an hour to do the same job, we can say that the number of men and the time are in inverse proportion, or that these quantities are inversely proportional. 36% (thirty-six percent) is really a fraction with a numerator of thirty-six and a 8denominator of one hundred. The farction expressed as a percentage is 20%. If a 40number is decreased by 10%, the ratio of the new number to the old number is 90 : 100. If a number is increased by 10%, the ratio of the new number to the old number is 110 : 100. If we borrow a sum of money at a rate of interest of 10%, we must pay back the money in the same proportion. If a student scores 81% in one exam and 87% in the next, his average (or mean) percentage is 84%. Practice 1.C 1. Answer these question. a. Which fraction with a denominator of sxteen is in proportion to one over four? b. If a plan is drawn to a scale of 1 : 50 (one to fifty), what is the actual measurement which is shown on the plan as four centimetres? c. Divide one hundred and forty sheep into two groups in the ratio of 3 : 4. d. The scale of a map is five centimetres to one kilometre. What is the representative fraction of the map? e. On the same map, what length will represent nine kilometres? f. Divide thirty-six pounds into three parts in the ratio 6 : 5 : 1. g. Five families have a total of 100 sheep. How many sheep will six families have if the numbers are in proportion? h. A concrete mix of cement, sand and gravel is made in the ratio of 2 : 5 : 8. What is the weight of each part in thirty tonnes of concrete? i. In a class of student the ratio of successes to falures in an examination was 9 : 2. If eighteen students passed the examination, how many failed? j. If ten litres of oil weigh eight kilograms, and a litre of water weighs one kilogram, what is the ratio of the relative density of oil and water? 42. Answer these question. a. What is four and a half percent of eight hundred people? b. What is thirty percent of fifty? c. Express fifty-six as a percentage of seventy. d. What percentage is four fifths? e. What fraction is seventy-five percent? f. What decimal fraction is sixty-three point nine percent? g. What is the ratio of men to women if sixty percent are men? h. How much interest has a bank been paid if it receives a total of six fifths of the sum borrowed? i. In a class of twenty-five students, twenty come to school by bus and five by car. What is the ratio of those who come by car to those who come by bus, and what percentage of the class does each group represent? j. The numerator of a fraction is 6. This numerator is equal to thirty-three point three recurring percent of the denominator. What is the fraction? 3. Fill in the blank spaces in the following sentences: a. To convert a ---- to a fraction, divide ---- 100. b. If three metres of material cost 225 units of money and eight metres cost six hundred units of money, the lengths and prices are ---- ---- . c. If the plan of building is drawn to a ---- of 1 : 65, one centimetre on the plan ---- sixty-five centimetres on the building. d. In a certain country, rainy days and dry days are in the ---- 1 : 7. e. If we wish to ---- a vulgar ---- as a ---- , we must ---- by one hundred. 5Document Outline